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1 problem
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declared open
· formalized
erdos:522
For
P
n
(
z
)
=
∑
k
=
0
n
ε
k
z
k
P_n(z) = \sum_{k=0}^n \varepsilon_k z^k
with independent uniform signs, does the number
R
n
R_n
of roots in
∣
z
∣
≤
1
|z| \le 1
satisfy
R
n
/
(
n
/
2
)
→
1
R_n/(n/2) \to 1
almost surely? The manuscript proves the strong law with
R
n
=
n
/
2
+
O
ω
(
n
149
/
150
)
R_n = n/2 + O_\omega(n^{149/150})
.
analysis
polynomials
probability
N/A
4 sources
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